reserve a,b,r for non unit non zero Real;
reserve X for non empty set,
        x for Tuple of 4,X;
reserve V             for RealLinearSpace,
        A,B,C,P,Q,R,S for Element of V;

theorem
  for V being RealLinearSpace for x,y being Element of F_Real
  for x9,y9 being Element of V st V = F_Real & x = x9 & y = y9 holds
  x + y = x9 + y9;
